Nozha Directorate of Education Form : 2 nd Prep

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1 Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. In the parallelogram, each two opposite sides are.., 2. In the //gram, each two consecutive angles are. 3. The //gram whose diagonals are perpendicular is called 4. The parallelogram whose diagonals are equal in length and perpendicular is called 5. The rhombus whose diagonals are equal in length is called. 6. The rectangle whose diagonals are perpendicular is called. 7. ABCD is a //gram in which m ( B ) = º 8. The two diagonals of the square are,.. 9. ABCD is a parallelogram in which m ( A ) + m ( C ) = 140 º 10. ABCD is a rectangle in which m ( A ) = 5x 10, then x = 2-Find The value of x, y and z :- 3-Find :- 1. The length of AM, BD, AD and BC 2. m ( A ), m ( B ) 4- in the opposite figure:- ABCD is a rectangle,fbce is a //gram Prove that : AF = DE 5- in the opposite figure:- ABCD, BEFC are two //grams Find m( ABE )

2 6- in the opposite figure :- Prove that ABCD is a //gram D A 110 C 70 B 7- in the opposite figure :- ABCD is a //gram in which BE = BC, DE = DC Prove that:- ABCD is a rectangle

3 Sheet 2 1- complete:- 1. The medians of the triangle intersect at 2. The no. of medians in the right angled triangle is 3. The length of the median from the vertex of the right angle in the right angled =. 4. The length of the hypotenuse in thirty and sixty triangle =.. the length of the side opposite the angle whose measure is 30 º 5. The line segment drawn between the two midpoints of two sides in a triangle is. And its length = 2- in the opposite figure :- DE = 4 cm, DM = 3 cm and BE = 6 cm Find the perimeter of BMC 3- in the opposite figure:- If m ( A ) = m ( D )= 90 º, M ( ACB ) = 30 º Prove that AB = DE 4- in the opposite figure :- Prove that YM = DE

4 5- in the opposite figure :- AB = DE Prove that m ( ADC ) = 90 º 6- in the opposite figure :- Prove that DFE is an isosceles 7- in the opposite figure :- Find the length of each of AB, XY and BZ

5 Sheet 3 Complete 1- In the isosceles if the measure of one of the two base angles 65º then the measure of its vertex angle = 2- In the isosceles if the vertex angle = 50 º then the measure of one of the two base angles =.. 3- If ABC is right angled at A, AB =AC then m ( B ) =.. 4- In XYZ if XY = XZ, then the exterior angle at the vertex Z is 5- In XYZ if XY = YZ = ZX, then m ( X ) =.º Find :- a) m ( D ) b) m ( CAD ) In the opposite figure :- AC = AB, CE = ED = CD Find m ( BCD ) Find :- m( MLY )

6 prove that :- AE bisects ( DAC ) Find the measure of the measures of the angles of ABC Find The value of X in the following figures:-

7 Sheet 4 Complete 1- If two angles in the triangle are congruent then the two sides opposite these two angles are and the triangle is. 2- If the three angles in the triangle are congruent then the triangle is 3- If the isosceles has angle = 45º, then the is 4- In ABC if AC = CB and m ( C ) m ( A ), then m ( B ) =.º 5- ABC is m ( A) = 30 º, m ( B ) : m ( C ) = 1 : 4 then ABC is 2- in the opposite figure :- MB=MC, AD // BC Prove that MA = MD 3- prove that AB = AC 4- in the opposite figure :- m( D ) = m ( E)=90º m( ABC) =m( ACB) Prove that m( DAB) = m( CAE)

8 5- BY=CZ, m ( B ) = m ( Z ) Prove that EYC is an isosceles 6- m( B) = ( C) find the perimeter of 7-ABCD is rectangle BF = CL Prove that: 1) AF = DL 2) EFL is an isosceles 8-ABCD is a square m ( MBC) = m ( MCB) Prove that AMD is an isosceles

9 9- m ( A ) = m ( B ), ED // AC ED = 2 1 AC Prove that :- m ( BEC ) = 90

10 Sheet 5 Complete 1- The straight line drawn from the vertex of the isosceles perpendicular to the base is called.. 2- The median of the isosceles drawn from the vertex. 3- The bisector of the vertex angle of the isosceles.. 4- The st. line drawn from the vertex of an isosceles its base 5- Any point the axis of the line segment is from its two terminals 6- If C the axis of symmetry of AB then = AC 7- The triangle whose angles are congruent has.. axes of symmetry 8- In ABC if m ( A ) = m ( B ) 60 then the no. of axes of symmetry of triangle ABC is 9- If the length of each sides in the triangle = 3 1 the perimeter of triangle then the no. of axes of symmetry of triangle is. 10- If ABCD is a rhombus then the axis of symmetry of AC is. 2- AB = AC, D and E are two midpoints of AB and AC Prove that 1- AM BC 2- AM bisects BAC 3-AC = AB, AB bisects BAC Prove that 1- BE = 2 1 BC 2- BC = CD

11 4-AD // BC, AE bisects BAD Prove that 1- AB =AD 2- AE BD 3- BE = ED 3- m ( ABD ) = m ( ACD ) AB = AC Prove that AD is the axis of symmetry of BC 4- AB = AC, BF bisects DBC, CF bisects BCE Prove that 1- BFC is an isosceles 2- AF is the axis of symmetry of BC

12 Sheet 6 1- Draw the isosceles triangle ABC which AB =AC using compasses, bisect BC at D. draw AD and prove that AD BC 2- Draw the equilateral ABC in which the length of each side is 4 cm then draw CD CB that intersect BA at D. find by proof length of AD 3- Draw ABC in which AB = 6 cm, m ( A ) = 50, m ( B ) = 70. Using the compasses and ruler draw XY passing through A and parallel to BC 4- Draw ABC with measure 60. bisect angle ABC from C draw CE // BA to meet the bisector of the angle at E, from E draw EF BA where EF BA = { F } prove that m ( ABC ) = m ( FEB ) 5- Draw any triangle bisect each B, C then draw AE // BC to meet the bisector of B at E and the bisector of C at F. prove that ABC is an isosceles triangle and FE = AB + AC

13 1- M bisects each of AC, BD Prove that m ( ABE) > m ( ACD) Sheet 7 2- AC > AB m ( AXY) = m( AYX) Prove that YC > XB 3- XY > XL, YZ > ZL Prove that m( XLZ) > m( XYZ) 4- AB = AC, BD > DC Prove that m( ABD) > m( ACD)

14 5- AB > AC, XY// BC Prove that m( AYX) > m(axy) 6- AB > AC BF bisects DBC CF bisects BCE Prove that m( FBC) > m( BCF) 7- prove that a) m ( ABC) > m ( ADC) b) m( BCD) > m( BAD) c) m( B) + m( C) > BM < AM Prove that ABC is an obtuse angle.

15 Sheet 8 1-Complete 1) The smallest angle of triangle (in measure ) is opposite to.. 2) The longest side in the right angle triangle is. 3) If triangle ABC m ( A) =50 m ( B) =30 4) If in triangle ABC m ( A) = m ( B) +m ( C) then the longest side in the triangle is.. 5) in the triangle ABC if m ( B) > m ( C) then.<. 2-AC CD, BD CD Prove that AB > CD 3- AB > AC, YX // BC XM bisects AYX Prove that XM > MY 4- AB = AD m( D ) > m( B ) prove that BC > CD

16 5- AB=BD=DF Prove that BC > A 6- prove that a) BD = DE b) DC > DB

17 Sheet 9 choose the correct answer :- 1-The lengths of any side in a triangle the sum of lengths of the two other sides a) > b) < c) = d) twice 2- Which of the following no. cannot be the lengths of sides of a triangle a) 7,7,5 b) 9,9,9 c) 3,6,12 d) 3, 4,5 3-If the lengths of two sides of an isosceles triangle are 3cm, 7cm then the length of the third side a) 7 cm b) 3 cm c) 4 cm d) 10 cm 4-In ABC AB + BC AC a) > zero b) < zero c) = zero d) = the perimeter of ABC 6-Is it possible to draw a triangle whose side length are as follows a) 5 cm, 7 cm, 8 cm b) 9 cm, 9 cm, 19 cm c) 5 cm, 3 cm, 4 cm Find the interval to which the length of the third side of :- a) 6 cm, 9 cm b) 5.7 cm, 7.3 cm c) 3 cm, 3 cm 1- prove that : MA + MB + MC > 2 1 the perimeter of ABC 2- ABCD is quadrilateral Prove that AB + BC + CD > AD

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite